`scipy.stats._multivariate:multivariate_normal_gen`

source: /scipy/stats/_multivariate.py :346

Signature

class multivariate_normal_gen ( seed = None )

Members

Summary

A multivariate normal random variable.

Extended Summary

The mean keyword specifies the mean. The cov keyword specifies the covariance matrix.

Parameters

%(_mvn_doc_default_callparams)s
%(_doc_random_state)s

Methods

pdf(x, mean=None, cov=1, allow_singular=False): Probability density function.
logpdf(x, mean=None, cov=1, allow_singular=False): Log of the probability density function.
cdf(x, mean=None, cov=1, allow_singular=False, maxpts=1000000*dim, abseps=1e-5, releps=1e-5, lower_limit=None): Cumulative distribution function.
logcdf(x, mean=None, cov=1, allow_singular=False, maxpts=1000000*dim, abseps=1e-5, releps=1e-5): Log of the cumulative distribution function.
rvs(mean=None, cov=1, size=1, random_state=None): Draw random samples from a multivariate normal distribution.
entropy(mean=None, cov=1): Compute the differential entropy of the multivariate normal.
marginal(dimensions, mean=None, cov=1, allow_singular=False): Return a marginal multivariate normal distribution.
fit(x, fix_mean=None, fix_cov=None): Fit a multivariate normal distribution to data.

Notes

%(_mvn_doc_callparams_note)s

The covariance matrix cov may be an instance of a subclass of Covariance, e.g. scipy.stats.CovViaPrecision. If so, allow_singular is ignored.

Otherwise, cov must be a symmetric positive semidefinite matrix when allow_singular is True; it must be (strictly) positive definite when allow_singular is False. Symmetry is not checked; only the lower triangular portion is used. The determinant and inverse of cov are computed as the pseudo-determinant and pseudo-inverse, respectively, so that cov does not need to have full rank.

The probability density function for multivariate_normal is

f (x) = \frac{1}{( 2 π ) ^{k} det Σ} exp (- \frac{1}{2} (x - μ)^{T} Σ^{- 1} (x - μ)),

where $μ$ is the mean, $Σ$ the covariance matrix, $k$ the rank of $Σ$ . In case of singular $Σ$ , SciPy extends this definition according to ^[1].

Examples

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import multivariate_normal

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x = np.linspace(0, 5, 10, endpoint=False)

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y = multivariate_normal.pdf(x, mean=2.5, cov=0.5); y

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fig1 = plt.figure()
ax = fig1.add_subplot(111)

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ax.plot(x, y)

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plt.show()

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Alternatively, the object may be called (as a function) to fix the mean and covariance parameters, returning a "frozen" multivariate normal random variable:

rv = multivariate_normal(mean=None, cov=1, allow_singular=False)

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The input quantiles can be any shape of array, as long as the last axis labels the components. This allows us for instance to display the frozen pdf for a non-isotropic random variable in 2D as follows:

x, y = np.mgrid[-1:1:.01, -1:1:.01]
pos = np.dstack((x, y))
rv = multivariate_normal([0.5, -0.2], [[2.0, 0.3], [0.3, 0.5]])
fig2 = plt.figure()
ax2 = fig2.add_subplot(111)

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ax2.contourf(x, y, rv.pdf(pos))

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Aliases

scipy.stats._multivariate.multivariate_normal_gen